When I stretch my object its open
When learning Blender, it is very easy to press one wrong key and have things change in strange and confusing ways. My guess is you accidentally pressed V, which ripped those vertices, causing the issue you now have when you later scaled or moved those vertices.
To solve this, you need to merge them again. First go to the menus at the bottom of the 3d viewer, and select Active Element from the pop-up menu that appears when you click the third field from the left. Now transforms are calculated according to the position of the active selected item, in this case the last vertex you select.

Now select the 3 vertices that have split open, by pressing RMB over one, then Shift + RMB over the other two. Select the one where you want the other two to merge to last.
Now press Alt + M, and from the pop-up, select At Last. The three vertices are now merged into one vertex, at the position of that last vertex.
A good habit when modelling is to try to reduce problems like this by occasionally selecting everything by pressing A, then pressing W &gt; Remove Doubles, pressing Ctrl + N to recalculate normals. Also whenever you switch between Edit and Object modes, press A until you are sure nothing is selected, otherwise the next time you edit that object, you may be changing things you don't realize you have selected.